a cyclist enters a curve at 28m radius at a speed of 16ms. he applies the brakes, and decreases his speed at a constant rate of 0.6ms. calculate the cyclist's centripetal radial and tangential accelerations when he is traveling at a speed of 13ms.
First, let's calculate the centripetal acceleration:
Centripetal acceleration \(a_c = \frac{v^2}{r}\),
\(a_c = \frac{(13 ms)^2}{28m}\),
\(a_c = \frac{169 ms^2}{28m}\),
\(a_c = 6.04 ms^2\).
Now, let's calculate the radial acceleration:
Radial acceleration \(a_r = - \frac{dv}{dt}\),
Given that the cyclist is decreasing his speed at a constant rate of 0.6 ms,
\(a_r = -0.6 ms^{-2}\).
Lastly, let's calculate the tangential acceleration:
Tangential acceleration \(a_t = \frac{dv}{dt} = -0.6 ms^{-2}\).
Therefore, when the cyclist is traveling at a speed of 13ms, his centripetal acceleration is 6.04ms^2, his radial acceleration is -0.6ms^2, and his tangential acceleration is also -0.6ms^2.